Feb 5, 1986.
Dear Milne,
I sent you the texts you acknowledge receipt of, because you are named there as a
participant of a fraud, and I thought you might wish to give some explanation. The
part of the text which most concerns you is on pages 832-38, 1108-10, 1170-73. The text
is going to the printer by the end of this month, and I'll mention in a footnote whether
or not the "préjudice de bonne foi" I had been keeping with respect to you, Ogus and Shih,
has been substantiated or not by the response or non-response I got.
Yours sincerely
A Grothendieck.
13th February, 1986
Dear Grothendieck,
Those parts of "L'ENTERREMENT" that I have read concerning Lecture Notes 900 are pure phantasy
and are deeply insulting to both Deligne and me.
I can assure you that there is no conspiracy to "bury" either you or your mathematics. It is
entirely a figment of your imagination.
Your question of whether my writings are in "bonne foi", that is, whether they were written
without the deliberate design of "enterrement", is too silly to merit a response.
I hope that, having completed this work, you can now turn your attention to more fruitful
activities.
Yours sincerely,
J. S. Milne
I give one example. When Deligne and I were discussing the Lecture Notes 900 volume,
I suggested that we include a 50 page exposition on Tannakian categories because,
at the time, the only source for them was Saavedra's 400 page thesis, which is difficult to
read. Deligne agreed, so we wrote the article, which has proved to be quite useful
to mathematicians wishing to learn the topic.
Compare this with Grothendieck's page after page of
conspiratorial fantasies.
Another example. Grothendieck goes on endlessly about how Deligne had "buried" motives until 1982, working "tirelessly at hiding the inheritance, denying and destructing the creative unity at its core" (R&S p379). However, in his 1977 Corvallis talk, Deligne "dreams" of realizing Shimura varieties as moduli varieties for motives, and I can recall many discussions in the 1970s with him on motives and Shimura varieties.
In fact, motives were everywhere in the 1970s --- Demazure had given a Bourbaki talk on them in November 1969 ("La notion de motif a été introduite par Grothendieck...") and Manin (Mat. Sb. 1968) explains them ("I learned about the theory of motifs from lectures of Grothendieck at I.H.E.S. (Paris) in the spring of 1967). They even occur in the title of Langlands's 1977 Corvallis talk. Since everyone knew that motives were one of Grothendieck's great ideas, no one needed to mention it.
Grothendieck didn't like Grothendieck topologies because two such topologies may give the same sheaf theory, which was what was important, so he called them "pre-topologies" and gave a new definition of "topology". But the new definition has the same problem, so he concluded that the essential object is the category of sheaves of sets, which he called a topos. When the original typed notes for SGA 4 were published by Springer, hundreds of pages of topos theory had been added (112 pages became 512). However, pre-topologies are perfectly adequate for étale cohomology, and have the advantage of making the theory look more like the usual cohomology theory on topological spaces. Since topos theory was irrelevant for the mathematics we were interested in, many of us simply ignored it. Grothendieck was so offended by this that he concluded that we must all be part of some large conspiracy to bury him and his mathematics. This, of course, was nonsense: we just weren't interested in topos theory.
For all its flaws, R&S contains some beautiful writing:
Mon principal guide dans mon travail a été la recherche constante d'une cohérence parfaite, d'une harmonie complète que je devinais derrière la surface turbulente des choses, et que je m'efforçais de dégager patiemment, sans jamais m'en lasser. C'était un sens aigu de la "beauté", súrement, qui était mon flair et ma seule boussole. Ma plus grande joie a été, moins de la contempler quand elle était apparue en pleine lumière, que de la voir se dégager peu à peu du manteau d'ombre et de brumes où il lui plaisait de se dérober sans cesse. Certes, je n'avais de cesse que quand j'étais parvenu à l'amener jusqu'à la plus claire lumière du jour. J'ai connu alors, parfois, la plénitude de la contemplation, quand tous les sons audibles concourent à une même et vaste harmonie. Mais plus souvent encore, ce qui était amené au grand jour devenait aussitot motivation et moyen d'une nouvelle plongée dans les brumes, à la poursuite d'une nouvelle incarnation de Celle qui restait à jamais mystérieuse, inconnue --- m'appelant sans cesse...[Because a version of R&S has been published, I decided that it was time to make public what those of us who were around in the sixties and seventies have been saying privately.]My principal guide has been the constant search for a perfect coherence, a complete harmony, that I sensed lay behind the turbulent surface of things, and that I endeavoured to release patiently, tirelessly. A keen sense of "beauty", certainly, guided my instincts and was my only compass. My greatest joy was not so much in contemplating it when it had been brought into the full light, as in seeing it gradually emerge from the cloak of shadow and mist where it liked to hide. Of course, I did not stop until I had managed to bring it into the clearest light of day. I knew then, sometimes, the fullness of contemplation, when all heard sounds contribute to a single vast harmony. But more often, what had been brought into the light immediately became the motivation and means for a new plunge into the mists, in pursuit of a new incarnation of That which remained forever mysterious, unknown --- calling me constantly.
For an excellent article on R&S by Pierre Schapira, see here (posted as arXiv:2301.02898).